AUCTORES
Globalize your Research
Short Review | DOI: https://doi.org/10.31579/2690-1919/117
*Corresponding Author: Dongfeng Wu, Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, KY 40202.
Citation: Dongfeng Wu, Seongho Kim, Problems in the Estimation of the Key Parameters using MLE in Lung Cancer Screening. J Clinical Research and Reports, 5(3); DOI:10.31579/2690-1919/117
Copyright: © 2020 Dongfeng Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: 11 August 2020 | Accepted: 18 August 2020 | Published: 21 August 2020
Keywords: lung cancer screening; MLE; NLST
We have been working in the area of cancer screening modeling for many years. A well-known and frequently used model in cancer screening is the progressive three-state model [1], where all cancer patients are assumed to go through three states: the disease-free state when one is cancer-free or the cancer is in an early stage that no technology can find; the preclinical state when one without symptom but cancer could be detected by screening, and the clinical state when cancer related symptoms show up. There are three key parameters in the model: a) the screening sensitivity, the probability of a positive screening result given that one is in the preclinical state; b) the distribution of sojourn time, which measures the time duration in the preclinical state; and c) the transition density, which measures the time duration in the disease-free state, or the onset age of the preclinical state. These three parameters are called the key parameters since they determines the screening processes and all other terms, for example, lead time (diagnosis time advanced by screening), probability of over-diagnosis, etc., are functions of these three. Therefore accurate estimation of these three key parameters is critical and lays a foundation for all other estimations.
This is a short review article on the problems that we have encountered in the parameter estimation using likelihood functions and MLE in lung cancer screening. We also provide some ideas on how to fix these problems in practice.
We have been working in the area of cancer screening modeling for many years. A well-known and frequently used model in cancer screening is the progressive three-state model [1], where all cancer patients are assumed to go through three states: the disease-free state when one is cancer-free or the cancer is in an early stage that no technology can find; the preclinical state when one without symptom but cancer could be detected by screening, and the clinical state when cancer related symptoms show up. There are three key parameters in the model: a) the screening sensitivity, the probability of a positive screening result given that one is in the preclinical state; b) the distribution of sojourn time, which measures the time duration in the preclinical state; and c) the transition density, which measures the time duration in the disease-free state, or the onset age of the preclinical state. These three parameters are called the key parameters since they determines the screening processes and all other terms, for example, lead time (diagnosis time advanced by screening), probability of over-diagnosis, etc., are functions of these three. Therefore accurate estimation of these three key parameters is critical and lays a foundation for all other estimations.
A commonly used method to estimate the three key parameters is to use a likelihood function and the maximum likelihood estimate (MLE) [2-7]. However, when the number of the screening is less than four, it is very hard for the MLE to be close to the true value of the input parameters in any single run based on our simulation study. What we did was: step 1, generate pseudo screening data using some fixed input parameters; step 2, using the generated pseudo data and the likelihood to calculate the MLE; step 3, repeat the first two steps N (≥ 200) times, and compare the average of the MLE with the input parameters, and measure the errors in terms of the mean and the standard deviation. It turns out that unless a large sample size (such as 105) for each age group is used and unless the number of screening is at least 4, the average of the estimate MLE won’t be very close to the true input value; In the case of the large sample size, even though the average of MLE is close to the true input values, it still has a large standard error. Hence, for a single collected screening dataset, it is very hard to say whether the MLE is close to the true parameters.
The major problems for using the likelihood function and its MLE is: it is often a plateau-shaped function of the parameters with many local maxima (or minima), especially for sensitivity. In another word, a deterministic method to find the maximum (or minimum if you use the negative of the likelihood) is not sensitive enough. It depends on the initial values and very likely to find a local maximum (or minimum) after a finite iterations. To correct this, we have tried different initial values, developed different kinds of likelihoods, using conditional probabilities, hoping to improve it. However, the improvement is negligible.
This is what we have found: 1. Smaller sample size (population in each age group should be at least 10,000 in the simulation) cannot achieve much accuracy. In fact, standard deviation is much larger than the mean difference, showing that the variation is too large. In reality, sample size in each age group for existing screening program is much smaller. For example, in the recently finished National Lung Screening Trial (NLST) low dose CT arm, the largest two age groups has about 2600 participants each at initial screening, and it is usually less than 2000 in other age groups, with some of the age group has less than 500 participants. 2. Using conditional likelihood won’t improve the accuracy. Since there are many people dropped out of the screening program in the middle of the process, we thought maybe using conditional probability at each screening could handle the dropout problems better; the result is not significant, especially when the screening program only has 3 or fewer exams, such as in the NLST study. The reason may be due to the fact that since the screening number is fewer, and the screening interval is one year apart, the conditional probability of be asymptomatic before each screening is close to 1, making it the same as using the unconditional probability.
The most annoying problem is that the MLE estimate of screening sensitivity is over-estimated. This is especially obvious in the chest X-ray screening data in the PLCO [3] and the NLST study [4]. In the NLST study, the screening program composed of three annual exams, and there are two randomly assigned arms, chest X-ray and low-dose CT. Just looking at the screen-detected number and the interval-incident number, we can roughly estimate the sensitivity by dividing the screen-detected number with the total diseased cases (screen-detected cases plus interval cases), and know that low-dose CT has a much high sensitivity which is above 90%, while chest X-ray has a lower sensitivity between 60-70%. And due to the random assignment of participants, it is reasonable to assume that the two groups of participants share some common characteristics, such as both are heavy smokers, hence the estimated parameters regarding the sojourn time and the transition density should be close to each other. And the only difference should be in the screening sensitivity. However, it turns out, the estimated MLE of sensitivity from both groups are both close to 1, which is definitely untrue for the X-ray group. And we have to put some upper limit to get a reasonable estimate for the sensitivity for the X-ray group.
So how we are going to deal with these problems and get a reasonably accurate estimate of the key parameters? The best way is to use Bayesian posterior samples, and also put some reasonable limit or boundary on the sensitivity. A great advantage of the Bayesian posterior samples is that it is not focus on one specific point as an estimate, but reflects the posterior distribution of the sensitivity and its variation. It is also important to put a reasonable boundary for sensitivity based on the epidemiology result, so we can get the posterior samples of sensitivity in a reasonable range and reflects the true and not inflated distribution. Finally, a suggestion to future mass screening program investigators/designer or policy makers are: to apply at least 4 screenings, not three or less; otherwise, it is difficult to use the screening data and obtain meaningful information from it.
Acknowledgement
This short review was partially supported by the NIH/NCI 1R15CA242482.
Clearly Auctoresonline and particularly Psychology and Mental Health Care Journal is dedicated to improving health care services for individuals and populations. The editorial boards' ability to efficiently recognize and share the global importance of health literacy with a variety of stakeholders. Auctoresonline publishing platform can be used to facilitate of optimal client-based services and should be added to health care professionals' repertoire of evidence-based health care resources.
Journal of Clinical Cardiology and Cardiovascular Intervention The submission and review process was adequate. However I think that the publication total value should have been enlightened in early fases. Thank you for all.
Journal of Women Health Care and Issues By the present mail, I want to say thank to you and tour colleagues for facilitating my published article. Specially thank you for the peer review process, support from the editorial office. I appreciate positively the quality of your journal.
Journal of Clinical Research and Reports I would be very delighted to submit my testimonial regarding the reviewer board and the editorial office. The reviewer board were accurate and helpful regarding any modifications for my manuscript. And the editorial office were very helpful and supportive in contacting and monitoring with any update and offering help. It was my pleasure to contribute with your promising Journal and I am looking forward for more collaboration.
We would like to thank the Journal of Thoracic Disease and Cardiothoracic Surgery because of the services they provided us for our articles. The peer-review process was done in a very excellent time manner, and the opinions of the reviewers helped us to improve our manuscript further. The editorial office had an outstanding correspondence with us and guided us in many ways. During a hard time of the pandemic that is affecting every one of us tremendously, the editorial office helped us make everything easier for publishing scientific work. Hope for a more scientific relationship with your Journal.
The peer-review process which consisted high quality queries on the paper. I did answer six reviewers’ questions and comments before the paper was accepted. The support from the editorial office is excellent.
Journal of Neuroscience and Neurological Surgery. I had the experience of publishing a research article recently. The whole process was simple from submission to publication. The reviewers made specific and valuable recommendations and corrections that improved the quality of my publication. I strongly recommend this Journal.
Dr. Katarzyna Byczkowska My testimonial covering: "The peer review process is quick and effective. The support from the editorial office is very professional and friendly. Quality of the Clinical Cardiology and Cardiovascular Interventions is scientific and publishes ground-breaking research on cardiology that is useful for other professionals in the field.
Thank you most sincerely, with regard to the support you have given in relation to the reviewing process and the processing of my article entitled "Large Cell Neuroendocrine Carcinoma of The Prostate Gland: A Review and Update" for publication in your esteemed Journal, Journal of Cancer Research and Cellular Therapeutics". The editorial team has been very supportive.
Testimony of Journal of Clinical Otorhinolaryngology: work with your Reviews has been a educational and constructive experience. The editorial office were very helpful and supportive. It was a pleasure to contribute to your Journal.
Dr. Bernard Terkimbi Utoo, I am happy to publish my scientific work in Journal of Women Health Care and Issues (JWHCI). The manuscript submission was seamless and peer review process was top notch. I was amazed that 4 reviewers worked on the manuscript which made it a highly technical, standard and excellent quality paper. I appreciate the format and consideration for the APC as well as the speed of publication. It is my pleasure to continue with this scientific relationship with the esteem JWHCI.
This is an acknowledgment for peer reviewers, editorial board of Journal of Clinical Research and Reports. They show a lot of consideration for us as publishers for our research article “Evaluation of the different factors associated with side effects of COVID-19 vaccination on medical students, Mutah university, Al-Karak, Jordan”, in a very professional and easy way. This journal is one of outstanding medical journal.
Dear Hao Jiang, to Journal of Nutrition and Food Processing We greatly appreciate the efficient, professional and rapid processing of our paper by your team. If there is anything else we should do, please do not hesitate to let us know. On behalf of my co-authors, we would like to express our great appreciation to editor and reviewers.
As an author who has recently published in the journal "Brain and Neurological Disorders". I am delighted to provide a testimonial on the peer review process, editorial office support, and the overall quality of the journal. The peer review process at Brain and Neurological Disorders is rigorous and meticulous, ensuring that only high-quality, evidence-based research is published. The reviewers are experts in their fields, and their comments and suggestions were constructive and helped improve the quality of my manuscript. The review process was timely and efficient, with clear communication from the editorial office at each stage. The support from the editorial office was exceptional throughout the entire process. The editorial staff was responsive, professional, and always willing to help. They provided valuable guidance on formatting, structure, and ethical considerations, making the submission process seamless. Moreover, they kept me informed about the status of my manuscript and provided timely updates, which made the process less stressful. The journal Brain and Neurological Disorders is of the highest quality, with a strong focus on publishing cutting-edge research in the field of neurology. The articles published in this journal are well-researched, rigorously peer-reviewed, and written by experts in the field. The journal maintains high standards, ensuring that readers are provided with the most up-to-date and reliable information on brain and neurological disorders. In conclusion, I had a wonderful experience publishing in Brain and Neurological Disorders. The peer review process was thorough, the editorial office provided exceptional support, and the journal's quality is second to none. I would highly recommend this journal to any researcher working in the field of neurology and brain disorders.
Dear Agrippa Hilda, Journal of Neuroscience and Neurological Surgery, Editorial Coordinator, I trust this message finds you well. I want to extend my appreciation for considering my article for publication in your esteemed journal. I am pleased to provide a testimonial regarding the peer review process and the support received from your editorial office. The peer review process for my paper was carried out in a highly professional and thorough manner. The feedback and comments provided by the authors were constructive and very useful in improving the quality of the manuscript. This rigorous assessment process undoubtedly contributes to the high standards maintained by your journal.
International Journal of Clinical Case Reports and Reviews. I strongly recommend to consider submitting your work to this high-quality journal. The support and availability of the Editorial staff is outstanding and the review process was both efficient and rigorous.
Thank you very much for publishing my Research Article titled “Comparing Treatment Outcome Of Allergic Rhinitis Patients After Using Fluticasone Nasal Spray And Nasal Douching" in the Journal of Clinical Otorhinolaryngology. As Medical Professionals we are immensely benefited from study of various informative Articles and Papers published in this high quality Journal. I look forward to enriching my knowledge by regular study of the Journal and contribute my future work in the field of ENT through the Journal for use by the medical fraternity. The support from the Editorial office was excellent and very prompt. I also welcome the comments received from the readers of my Research Article.
Dear Erica Kelsey, Editorial Coordinator of Cancer Research and Cellular Therapeutics Our team is very satisfied with the processing of our paper by your journal. That was fast, efficient, rigorous, but without unnecessary complications. We appreciated the very short time between the submission of the paper and its publication on line on your site.
I am very glad to say that the peer review process is very successful and fast and support from the Editorial Office. Therefore, I would like to continue our scientific relationship for a long time. And I especially thank you for your kindly attention towards my article. Have a good day!
"We recently published an article entitled “Influence of beta-Cyclodextrins upon the Degradation of Carbofuran Derivatives under Alkaline Conditions" in the Journal of “Pesticides and Biofertilizers” to show that the cyclodextrins protect the carbamates increasing their half-life time in the presence of basic conditions This will be very helpful to understand carbofuran behaviour in the analytical, agro-environmental and food areas. We greatly appreciated the interaction with the editor and the editorial team; we were particularly well accompanied during the course of the revision process, since all various steps towards publication were short and without delay".
I would like to express my gratitude towards you process of article review and submission. I found this to be very fair and expedient. Your follow up has been excellent. I have many publications in national and international journal and your process has been one of the best so far. Keep up the great work.
We are grateful for this opportunity to provide a glowing recommendation to the Journal of Psychiatry and Psychotherapy. We found that the editorial team were very supportive, helpful, kept us abreast of timelines and over all very professional in nature. The peer review process was rigorous, efficient and constructive that really enhanced our article submission. The experience with this journal remains one of our best ever and we look forward to providing future submissions in the near future.
I am very pleased to serve as EBM of the journal, I hope many years of my experience in stem cells can help the journal from one way or another. As we know, stem cells hold great potential for regenerative medicine, which are mostly used to promote the repair response of diseased, dysfunctional or injured tissue using stem cells or their derivatives. I think Stem Cell Research and Therapeutics International is a great platform to publish and share the understanding towards the biology and translational or clinical application of stem cells.
I would like to give my testimony in the support I have got by the peer review process and to support the editorial office where they were of asset to support young author like me to be encouraged to publish their work in your respected journal and globalize and share knowledge across the globe. I really give my great gratitude to your journal and the peer review including the editorial office.
I am delighted to publish our manuscript entitled "A Perspective on Cocaine Induced Stroke - Its Mechanisms and Management" in the Journal of Neuroscience and Neurological Surgery. The peer review process, support from the editorial office, and quality of the journal are excellent. The manuscripts published are of high quality and of excellent scientific value. I recommend this journal very much to colleagues.
Dr.Tania Muñoz, My experience as researcher and author of a review article in The Journal Clinical Cardiology and Interventions has been very enriching and stimulating. The editorial team is excellent, performs its work with absolute responsibility and delivery. They are proactive, dynamic and receptive to all proposals. Supporting at all times the vast universe of authors who choose them as an option for publication. The team of review specialists, members of the editorial board, are brilliant professionals, with remarkable performance in medical research and scientific methodology. Together they form a frontline team that consolidates the JCCI as a magnificent option for the publication and review of high-level medical articles and broad collective interest. I am honored to be able to share my review article and open to receive all your comments.
“The peer review process of JPMHC is quick and effective. Authors are benefited by good and professional reviewers with huge experience in the field of psychology and mental health. The support from the editorial office is very professional. People to contact to are friendly and happy to help and assist any query authors might have. Quality of the Journal is scientific and publishes ground-breaking research on mental health that is useful for other professionals in the field”.
Dear editorial department: On behalf of our team, I hereby certify the reliability and superiority of the International Journal of Clinical Case Reports and Reviews in the peer review process, editorial support, and journal quality. Firstly, the peer review process of the International Journal of Clinical Case Reports and Reviews is rigorous, fair, transparent, fast, and of high quality. The editorial department invites experts from relevant fields as anonymous reviewers to review all submitted manuscripts. These experts have rich academic backgrounds and experience, and can accurately evaluate the academic quality, originality, and suitability of manuscripts. The editorial department is committed to ensuring the rigor of the peer review process, while also making every effort to ensure a fast review cycle to meet the needs of authors and the academic community. Secondly, the editorial team of the International Journal of Clinical Case Reports and Reviews is composed of a group of senior scholars and professionals with rich experience and professional knowledge in related fields. The editorial department is committed to assisting authors in improving their manuscripts, ensuring their academic accuracy, clarity, and completeness. Editors actively collaborate with authors, providing useful suggestions and feedback to promote the improvement and development of the manuscript. We believe that the support of the editorial department is one of the key factors in ensuring the quality of the journal. Finally, the International Journal of Clinical Case Reports and Reviews is renowned for its high- quality articles and strict academic standards. The editorial department is committed to publishing innovative and academically valuable research results to promote the development and progress of related fields. The International Journal of Clinical Case Reports and Reviews is reasonably priced and ensures excellent service and quality ratio, allowing authors to obtain high-level academic publishing opportunities in an affordable manner. I hereby solemnly declare that the International Journal of Clinical Case Reports and Reviews has a high level of credibility and superiority in terms of peer review process, editorial support, reasonable fees, and journal quality. Sincerely, Rui Tao.
Clinical Cardiology and Cardiovascular Interventions I testity the covering of the peer review process, support from the editorial office, and quality of the journal.
